>>John: >>Even humble Arithmetic is full of mystery and weirdness. >>For example, I'll bet it would take you less than 5 minutes >>to write a computer program that would search for the >>smallest even number greater that 4 that is not the sum of >>two primes (ignoring 1 and 2) and then stop. >>Question: Would your computer program ever stop? >>Answer: Nobody knows. >>Question: If the program never stops can we be sure there >>is some way to know >this, so we can give up and don't >>keep wasting computer time? >>Answer: No, Turing proved this is impossible.

>James: >The computer is a tool designed to do deterministic >computation. If you are foolhardy enough to try to do a >non-deterministic computation on a computer, you do so at >your own risk.

All algorithms are deterministic but not all algorithms are predictable. If
it's foolhardy to write or run the above program there is no way to tell
you're a fool in a finite amount of time. If it has not stopped at one
trillion perhaps it will stop at a trillion and two. It may have been running
for 10 billion years but that tells you nothing, 10 billion years is no closer
to being an infinite amount of time than one second is. It could stop in the
next 5 minutes, it might stop in another 99 trillion years, it might never
stop. There is no way to tell.

>In fact, I would submit that computers are *consciously >designed* in such a way as to be unable to solve >non-deterministic problems

Well, it's not like computer designers had any choice in the matter, it's
just the way things are. My program may well be able to solve its problem,
the point is there is no way to know if it can or can not except to run it,
and even then you can't even be sure. If it stops then you know, but if it
hasn't stopped yet, well maybe you just don't have enough patience.

>I still maintain that we understand arithmetic computation. >Not being able to solve a non-deterministic problem is by no >means contrary to this.

Why not?

>>John: >>How about trying to understand if a photon polarized at >>90 degrees will pass through a polarizer set at 45 degrees? >>Measure anything you want, look anywhere you want, compute >>anything you want, and it's still a crap shoot, the odds >>are 50 50. According to Quantum Physics the reason we don't >>understand some things is that there is nothing to >>understand, no reason, no cause, it's truly random.

>James: >This a measurement issue. Its a crap shoot because we can't >measure the exact state of the photon just prior to it >entering the polarizer. We can only measure the outcome.

Not so. I have a LASER that spits out photons at a random and unknown
polarization. I spin my polarizer, at random it is set at 63 degrees. When
the random photon hits my randomly set polarizer only 2 things can happen,
the polarizer can stop the photon or it can let it pass through, the chances
are exactly 50 50. If it passes through the polarizer I know the photon is
polarized at 63 degrees. How do I Know this? because if set another polarizer
at 63 degrees there is a 100% chance the photon will get through, it could
pass through a thousand of them. On the other hand if I set just one
polarizer at 153 degrees (63 +90) there is a 0% chance the photon will get
through. What about the intermediate case? If I set the polarizer at 108
degrees (63 +45) then the odds are 50 50 that the photon will get through
and there is nothing you can do to improve your certainty.